Methods and Apparatus For the Planning and Delivery of Radiation Treatments

ABSTRACT

Methods and apparatus are provided for planning and delivering radiation treatments by modalities which involve moving a radiation source along a trajectory relative to a subject while delivering radiation to the subject. In some embodiments the radiation source is moved continuously along the trajectory while in some embodiments the radiation source is moved intermittently. Some embodiments involve the optimization of the radiation delivery plan to meet various optimization goals while meeting a number of constraints. For each of a number of control points along a trajectory, a radiation delivery plan may comprise: a set of motion axes parameters, a set of beam shape parameters and a beam intensity.

CROSS-REFERENCE TO RELATED APPLICATION

This application claims priority from U.S. patent application No. 60/701,974 filed on 25 Jul. 2005, which is hereby incorporated herein by reference.

For purposes of the United States, this application claims the benefit under 35 U.S.C. §119 of U.S. patent application No. 60/701,974 filed on 25 Jul. 2005, which is hereby incorporated herein by reference.

TECHNICAL FIELD

This invention relates to radiation treatment. The invention relates particularly to methods and apparatus for planning and delivering radiation to a subject to provide a desired three-dimensional distribution of radiation dose.

BACKGROUND

The delivery of carefully-planned doses of radiation may be used to treat various medical conditions. For example, radiation treatments are used, often in conjunction with other treatments, in the treatment and control of certain cancers. While it can be beneficial to deliver appropriate amounts of radiation to certain structures or tissues, in general, radiation can harm living tissue. It is desirable to target radiation on a target volume containing the structures or tissues to be irradiated while minimizing the dose of radiation delivered to surrounding tissues. Intensity modulated radiation therapy (IMRT) is one method that has been used to deliver radiation to target volumes in living subjects.

IMRT typically involves delivering shaped radiation beams from a few different directions. The radiation beams are typically delivered in sequence. The radiation beams each contribute to the desired dose in the target volume.

A typical radiation delivery apparatus has a source of radiation, such as a linear accelerator, and a rotatable gantry. The gantry can be rotated to cause a radiation beam to be incident on a subject from various different angles. The shape of the incident radiation beam can be modified by a multi-leaf collimator (MLC). A MLC has a number of leaves which are mostly opaque to radiation. The MLC leaves define an aperture through which radiation can propagate. The positions of the leaves can be adjusted to change the shape of the aperture and to thereby shape the radiation beam that propagates through the MLC. The MLC may also be rotatable to different angles.

Objectives associated with radiation treatment for a subject typically specify a three-dimensional distribution of radiation dose that it is desired to deliver to a target region within the subject. The desired dose distribution typically specifies dose values for voxels located within the target. Ideally, no radiation would be delivered to tissues outside of the target region. In practice, however, objectives associated with radiation treatment may involve specifying a maximum acceptable dose that may be delivered to tissues outside of the target.

Treatment planning involves identifying an optimal (or at least acceptable) set of parameters for delivering radiation to a particular treatment volume. Treatment planning is not a trivial problem. The problem that treatment planning seeks to solve involves a wide range of variables including:

the three-dimensional configuration of the treatment volume;

the desired dose distribution within the treatment volume;

the locations and radiation tolerance of tissues surrounding the treatment volume; and

constraints imposed by the design of the radiation delivery apparatus.

The possible solutions also involve a large number of variables including:

the number of beam directions to use;

the direction of each beam;

the shape of each beam; and

the amount of radiation delivered in each beam.

Various conventional methods of treatment planning are described in:

-   S. V. Spirou and C.-S. Chui. A gradient inverse planning algorithm     with dose-volume constraints, Med. Phys. 25, 321-333 (1998); -   Q. Wu and R. Mohand. Algorithm and functionality of an intensity     modulated radiotherapy optimization system, Med. Phys. 27, 701-711     (2000); -   S. V. Spirou and C.-S. Chui. Generation of arbitrary intensity     profiles by dynamic jaws or multileaf collimators, Med. Phys. 21,     1031-1041 (1994); -   P. Xia and L. J. Verhey. Multileaf collimator leaf sequencing     algorithm for intensity modulated beams with multiple static     segments, Med. Phys. 25, 1424-1434 (1998); and -   K. Otto and B. G. Clark. Enhancement of IMRT delivery through MLC     rotation,” Phys. Med. Biol. 47, 3997-4017 (2002).

Acquiring sophisticated modern radiation treatment apparatus, such as a linear accelerator, can involve significant capital cost. Therefore it is desirable to make efficient use of such apparatus. All other factors being equal, a radiation treatment plan that permits a desired distribution of radiation dose to be delivered in a shorter time is preferable to a radiation treatment plan that requires a longer time to deliver. A treatment plan that can be delivered in a shorter time permits more efficient use of the radiation treatment apparatus. A shorter treatment plan also reduces the risk that a subject will move during delivery of the radiation in a manner that may significantly impact the accuracy of the delivered dose.

Despite the advances that have been made in the field of radiation therapy, there remains a need for radiation treatment methods and apparatus and radiation treatment planning methods and apparatus that provide improved control over the delivery of radiation, especially to complicated target volumes. There also remains a need for such methods and apparatus that can deliver desired dose distributions relatively quickly.

SUMMARY

One aspect of the invention provides a method for planning delivery of radiation dose to a target area within a subject. The method involves defining a set of one or more optimization goals which include a desired dose distribution in the subject. The method also involves specifying an initial plurality of control points along an initial trajectory which defines relative movement between a radiation source and the subject. The method comprises iteratively optimizing a simulated dose distribution relative to the set of optimization goals to determine one or more radiation delivery parameters associated with each of the initial plurality of control points. When the optimization relating to the initial plurality of control points reaches one or more initial termination conditions, the method comprises: adding one or more additional control points to obtain an increased plurality of control points; and iteratively optimizing the simulated dose distribution relative to the set of optimization goals to determine one or more radiation delivery parameters associated with each of the increased plurality of control points.

Another aspect of the invention provides a method for delivering radiation dose to a target area within a subject. The method involves defining a trajectory for relative movement between a radiation source and the subject and determining a radiation delivery plan. The method also involves, while effecting relative movement between the radiation source and the subject along the trajectory, delivering a radiation beam from the radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject. Delivering the radiation beam from the radiation source to the subject comprises varying an intensity of the radiation beam and varying a shape of the radiation beam over at least a portion of the trajectory. Effecting relative movement between the radiation source and the subject along the trajectory comprises one or more of: effecting non-planar relative movement between the radiation source and the subject; effecting continuous relative movement between the radiation source and the subject along the trajectory; effecting non-self-overlapping relative movement between the radiation source and the subject; wherein a start of the trajectory and an end of the trajectory comprise the same relative position between the radiation source and the subject and effecting otherwise non-self-overlapping relative movement between the radiation source and the subject; and moving a plurality of motion axes of a radiation delivery apparatus.

Another aspect of the invention provides a method for planning delivery of radiation dose to a target area within a subject. The method involves defining a set of one or more optimization goals which comprise a desired dose distribution in the subject. The method also involves defining an initial trajectory for relative movement between a radiation source and the subject and an initial plurality of control points along the initial trajectory. The method comprises iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points. The one or more radiation delivery parameters comprise a position of the radiation source relative to the subject, such that iteratively optimizing the simulated dose distribution comprises defining an optimized trajectory that is different from the initial trajectory for relative movement between the radiation source and the subject on the basis of the radiation delivery parameters.

Another aspect of the invention provides a method for planning delivery of radiation dose to a target area within a subject. The method involves defining a set of one or more optimization goals which include a desired dose distribution in the subject and defining a trajectory for relative movement between a radiation source and the subject and a plurality of control points along the trajectory. The method comprises iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points. The iterative optimization involves simulating a dose contribution for at least one particular control point by: dividing a cross-sectional area of a beam-shape aperture into a plurality of two-dimensional beamlets; and simulating a dose distribution contribution from each of the plurality of two-dimensional beamlets, wherein at least two of the plurality of two-dimensional beamlets have different sizes.

Another aspect of the invention provides a method for planning delivery of radiation dose to a target area within a subject. The method involves defining a set of one or more optimization goals which include a desired dose distribution in the subject. The method also involves specifying a plurality of control points along a trajectory which defines relative movement between a radiation source and the subject. The method comprises iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals to determine one or more radiation delivery parameters associated with each of the plurality of control points and, upon reaching one or more constraint-addition conditions, adding one or more optimization constraints to the iterative optimization to determine one or more radiation delivery parameters associated with each of the plurality of control points subject to the one or more optimization constraints.

Another aspect of the invention provides a method for delivering radiation dose to a target area within a subject. The method involves defining a trajectory for relative movement between a treatment radiation source and the subject and determining a radiation delivery plan. While effecting relative movement between the treatment radiation source and the subject along the trajectory, the method comprises: delivering a treatment radiation beam from the treatment radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject, wherein delivering the treatment radiation beam from the treatment radiation source to the subject comprises varying an intensity of the treatment radiation beam and varying a shape of the treatment radiation beam over at least a portion of the trajectory; and obtaining two-dimensional projection images of the target area at a plurality of locations along the trajectory.

Another aspect of the invention provides a method for delivering radiation dose to a target area within a subject. The method involves defining a trajectory for relative movement between a radiation source and the subject, determining a radiation delivery plan and sensing a positional state of the subject. While effecting relative movement between the radiation source and the subject along the trajectory, the method comprises delivering a radiation beam from the radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject. Delivering the radiation beam from the radiation source to the subject involves: varying an intensity of the radiation beam and varying a shape of the treatment radiation beam over at least a portion of the trajectory; deactivating delivery of the radiation beam upon sensing that the position of the subject is outside of an acceptable range; and reactivating delivery of the radiation beam upon sensing that the position of the subject is within the acceptable range.

Other aspects of the invention provide program products comprising computer readable instructions which, when executed by a processor, cause the processor to execute any of the methods summarized above and described in more detail below.

Further aspects of the invention and features of embodiments of the invention are set out below and illustrated in the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

The appended drawings illustrate non-limiting example embodiments of the invention.

FIG. 1 is a schematic view of an exemplary radiation delivery apparatus in conjunction with which the invention may be practised.

FIG. 1A is a schematic view of another exemplary radiation delivery apparatus in conjunction with which the invention may be practised.

FIG. 2 is a schematic illustration of a trajectory.

FIG. 3A is a schematic cross-sectional view of a beam-shaping mechanism.

FIG. 3B is a schematic beam's eye plan view of a multi-leaf collimator-type beam-shaping mechanism.

FIG. 4A is a flow chart illustrating a method of optimizing dose delivery according to a particular embodiment of the invention.

FIG. 4B is a schematic flow chart depicting a method for planning and delivering radiation to a subject according to a particular embodiment of the invention.

FIGS. 5A, 5B and 5C illustrate dividing an aperture into beamlets according to a particular embodiment of the invention.

FIG. 6 graphically depicts the error associated with a dose simulation calculation versus the number of control points used to perform the dose simulation calculation.

FIG. 7 graphically depicts dose quality versus the number of optimization iterations for several different numbers of control points.

FIG. 8 represents a flow chart which schematically illustrates a method of optimizing dose delivery according to another embodiment of the invention where the number of control points is varied over the optimization process.

FIG. 9 graphically depicts the dose distribution quality versus the number of iterations for the FIG. 8 optimization method where the number of control points is varied over the optimization process.

FIG. 10 is a depiction of sample target tissue and healthy tissue used in an illustrative example of an implementation of a particular embodiment of the invention.

FIGS. 11A and 11B respectively depict the initial control point positions of the motion axes corresponding to a trajectory used in the FIG. 10 example.

FIGS. 12A-12F depict a dose volume histogram (DVH) which is representative of the dose distribution quality at various stages of the optimization process of the FIG. 10 example.

FIG. 13 another graphical depiction of the optimization process of the FIG. 10 example.

FIGS. 14A-14D show the results (the motion axes parameters, the intensity and the beam shaping parameters) of the optimization process of the FIG. 10 example.

FIG. 15 plots contour lines of constant dose (isodose lines) in a two-dimensional cross-sectional slice of the target region in the FIG. 10 example.

DESCRIPTION

Throughout the following description specific details are set forth in order to provide a more thorough understanding to persons skilled in the art. However, well known elements may not have been shown or described in detail to avoid unnecessarily obscuring the disclosure. Accordingly, the description and drawings are to be regarded in an illustrative, rather than a restrictive, sense.

This invention relates to the planning and delivery of radiation treatments by modalities which involve moving a radiation source along a trajectory relative to a subject while delivering radiation to the subject. In some embodiments the radiation source is moved continuously along the trajectory while in some embodiments the radiation source is moved intermittently. Some embodiments involve the optimization of the radiation delivery plan to meet various optimization goals while meeting a number of constraints. For each of a number of control points along a trajectory, a radiation delivery plan may comprise: a set of motion axes parameters, a set of beam shape parameters and a beam intensity.

FIG. 1 shows an example radiation delivery apparatus 10 comprising a radiation source 12 capable of generating or otherwise emitting a beam 14 of radiation. Radiation source 12 may comprise a linear accelerator, for example. A subject S is positioned on a table or “couch” 15 which can be placed in the path of beam 14. Apparatus 10 has a number of movable parts that permit the location of radiation source 12 and orientation of radiation beam 14 to be moved relative to subject S. These parts may be referred to collectively as a beam positioning mechanism 13.

In the illustrated radiation delivery apparatus 10, beam positioning mechanism 13 comprises a gantry 16 which supports radiation source 12 and which can be rotated about an axis 18. Axis 18 and beam 14 intersect at an isocenter 20. Beam positioning mechanism 13 also comprises a moveable couch 15. In exemplary radiation delivery apparatus 10, couch 15 can be translated in any of three orthogonal directions (shown in FIG. 1 as X, Y, and Z directions) and can be rotated about an axis 22. In some embodiments, couch 15 can be rotated about one or more of its other axes. The location of source 12 and the orientation of beam 14 can be changed (relative to subject S) by moving one or more of the movable parts of beam positioning mechanism 13.

Each separately-controllable means for moving source 12 and/or orienting beam 14 relative to subject S may be termed a “motion axis”. In some cases, moving source 12 or beam 14 along a particular trajectory may require motions of two or more motion axes. In exemplary radiation delivery apparatus 10, motion axes include:

rotation of gantry 16 about axis 18;

translation of couch 15 in any one or more of the X, Y, Z directions; and

rotation of couch 15 about axis 22.

Radiation delivery apparatus 10 typically comprises a control system 23 capable of controlling, among other things, the movement of its motion axes and the intensity of radiation source 12. Control system 23 may generally comprise hardware components and/or software components. In the illustrated embodiment, control system 23 comprises a controller 24 capable of executing software instructions. Control system 23 is preferably capable of receiving (as input) a set of desired positions for its motion axes and, responsive to such input, controllably moving one or more of its motion axes to achieve the set of desired motion axes positions. At the same time, control system 23 may also control the intensity of radiation source 12 in response to input of a set of desired radiation intensities.

While radiation delivery apparatus 10 represents a particular type of radiation delivery apparatus in conjunction with which the invention may be implemented, it should be understood that the invention may be implemented on different radiation delivery apparatus which may comprise different motion axes. In general, the invention may be implemented in conjunction with any set of motion axes that can create relative movement between a radiation source 12 and a subject S, from a starting point along a trajectory to an ending point.

Another example of a radiation delivery apparatus 10A that provides an alternative set of motion axes is shown in FIG. 1A. In exemplary apparatus 10A, source 12 is disposed in a toroidal housing 26. A mechanism 27 permits source 12 to be moved around housing 26 to irradiate a subject S from different sides. Subject S is on a table 28 which can be advanced through a central aperture 29 in housing 26. Apparatus having configurations like that shown schematically in FIG. 1A are used to deliver radiation in a manner commonly called “Tomotherapy”.

In accordance with particular embodiments of the invention, beam positioning mechanism 13 causes source 12 and/or beam 14 to move along a trajectory while radiation dose is controllably delivered to target regions within subject S. A “trajectory” is a set of one or more movements of one or more of the movable parts of beam position mechanism 13 that results in the beam position and orientation changing from a first position and orientation to a second position and orientation. The first and second positions and the first and second orientations are not necessarily different. For example, a trajectory may be specified to be a rotation of gantry 16 from a starting point through an angle of 360° about axis 18 to an ending point in which case the beam position and orientation at the starting and ending points are the same.

The first and second beam positions and beam orientations may be specified by a first set of motion axis positions (corresponding to the first beam position and the first beam orientation) and a second set of motion axis positions (corresponding to the second beam position and the second beam orientation). As discussed above, control system 23 of radiation delivery apparatus 10 can controllably move its motion axes between the first set of motion axis positions and the second set of motion axis positions. In general, a trajectory may be described by more than two beam positions and beam orientations. For example, a trajectory may be specified by a plurality of sets of motion axis positions, each set of motion axis positions corresponding to a particular beam position and a particular beam orientation. Control system 23 can then controllably move its motion axes between each set of motion axis positions.

In general, a trajectory may be arbitrary and is only limited by the particular radiation delivery apparatus and its particular beam positioning mechanism. Within constraints imposed by the design of a particular radiation delivery apparatus 10 and its beam positioning mechanism 13, source 12 and/or beam 14 may be caused to follow an arbitrary trajectory relative to subject S by causing appropriate combinations of movements of the available motion axes. A trajectory may be specified to achieve a variety of treatment objectives. For example, a trajectory may be selected to have a high ratio of target tissue within the beam's eye view compared to healthy tissue within the beam's eye view or to avoid important healthy organs or the like.

For the purpose of implementing the present invention, it is useful to discretize a desired trajectory into a number of “control points” at various locations along the trajectory. A set of motion axis positions can be associated with each such control point. A desired trajectory may define a set of available control points. One way to specify a trajectory of radiation source 12 and/or beam 14 is to specify at a set of discrete control points at which the position of each motion axis is defined.

FIG. 2 schematically depicts a radiation source 12 travelling relative to a subject S along an arbitrary trajectory 30 in three-dimensions while delivering radiation dose to a subject S by way of a radiation beam 14. The position and orientation of radiation beam 14 changes as source 12 moves along trajectory 30. In some embodiments, the changes in position and/or direction of beam 14 may occur substantially continuously as source 12 moves along trajectory 30. While source 12 is moving along trajectory 30, radiation dose may be provided to subject S continuously (i.e. at all times during the movement of source 12 along trajectory 30) or intermittently (i.e. radiation may be blocked or turned off at some times during the movement of source 12 along trajectory 30). Source 12 may move continuously along trajectory 30 or may move intermittently between various positions on trajectory 30. FIG. 2 schematically depicts a number of control points 32 along trajectory 30. In some embodiments, the specification of trajectory 30 defines the set of available control points 32. In other embodiments, the set of control points 32 are used to define trajectory 30. In such embodiments, the portions of trajectory 30 between control points 32 may be determined (e.g. by control system 23) from control points 32 by a suitable algorithm.

In general, control points 32 may be specified anywhere along trajectory 30, although it is preferable that there is a control point at the start of trajectory 30, a control point at the end of trajectory 30 and that the control points 32 are otherwise spaced-apart along trajectory 30. In some embodiments of the invention, control points 32 are selected such that the magnitudes of the changes in the position of a motion axis over a trajectory 30 are equal as between control points 32. For example, where a trajectory 30 is defined as a 360° arc of gantry 16 about axis 18 and where the number of control points 32 along trajectory 30 is 21, then control points 32 may be selected to correspond to 0° (a starting control point), 360° (an ending control point) and 19 other control points at 18° intervals along the arc of gantry 16.

Although trajectory 30 may be defined arbitrarily, it is preferable that source 12 and/or beam 14 not have to move back and forth along the same path. Accordingly, in some embodiments, trajectory 30 is specified such that it does not overlap itself (except possibly at the beginning and end of trajectory 30). In such embodiments, the positions of the motion axes of the radiation delivery apparatus are not the same except possibly at the beginning and end of trajectory 30. In such embodiments, treatment time can be minimized (or at least reduced) by irradiating subject S only once from each set of motion axis positions.

In some embodiments, trajectory 30 is selected such that the motion axes of the radiation delivery device move in one direction without having to reverse directions (i.e. without source 12 and/or beam 14 having to be moved back and forth along the same path). Selection of a trajectory 30 involving movement of the motion axes in a single direction can minimize wear on the components of a radiation delivery apparatus. For example, in apparatus 10, it is preferable to move gantry 16 in one direction, because gantry 16 may be relatively massive (e.g. greater than 1 ton) and reversing the motion of gantry 16 at various locations over a trajectory may cause strain on the components of radiation delivery apparatus 16 (e.g. on the drive train associated with the motion of gantry 16).

In some embodiments, trajectory 30 is selected such that the motion axes of the radiation delivery apparatus move substantially continuously (i.e. without stopping). Substantially continuous movement of the motion axes over a trajectory 30 is typically preferable to discontinuous movement, because stopping and starting motion axes can cause wear on the components of a radiation delivery apparatus. In other embodiments, the motion axes of a radiation delivery apparatus are permitted to stop at one or more locations along trajectory 30. Multiple control points 32 may be provided at such locations to allow the beam shape and/or beam intensity to be varied while the position and orientation of the beam is maintained constant.

In some embodiments, trajectory 30 comprises a single, one-way, continuous 360° rotation of gantry 16 about axis 18 such that trajectory 30 overlaps itself only at its beginning and end points. In some embodiments, this single, one-way, continuous 360° rotation of gantry 16 about axis 18 is coupled with corresponding one-way, continuous translational or rotational movement of couch 15, such that trajectory 30 is completely non-overlapping.

Radiation delivery apparatus, such as exemplary apparatus 10 (FIG. 1) and 10A (FIG. 1A), typically include adjustable beam-shaping mechanisms 33 located between source 12 and subject S for shaping radiation beam 14. FIG. 3A schematically depicts a beam-shaping mechanism 33 located between source 12 and subject S. Beam-shaping mechanism 33 may comprise stationary and/or movable metal components 31. Components 31 may define an aperture 31A through which portions of radiation beam 14 can pass. Aperture 31A of beam-shaping mechanism 33 defines a two-dimensional border of radiation beam 14 in a plane normal to the direction of radiation from source 12 to the target volume in subject S. Control system 23 is preferably capable of controlling the configuration of beam-shaping mechanism 33.

One non-limiting example of an adjustable beam-shaping mechanism 33 comprises a multi-leaf collimator (MLC) 35 located between source 12 and subject S. FIG. 3B schematically depicts a suitable MLC 35. As shown in FIG. 3B, MLC 35 comprises a number of leaves 36 that can be independently translated into or out of the radiation field to define one or more apertures 38 through which radiation can pass. Leaves 36, which may comprise metal components, function to block radiation. In the illustrated embodiment, leaves 36 are translatable in the directions indicated by double-headed arrow 41. The size(s) and shape(s) of aperture(s) 38 may be adjusted by selectively positioning each leaf 36.

As shown in the illustrate embodiment of FIG. 3B, leaves 36 are typically provided in opposing pairs. MLC 35 is typically mounted so that it can be rotated to different orientations about an axis 37 that extends perpendicular to a plane of leaves 36. In the illustrated embodiment of FIG. 3B, axis 37 extends into and out of the page and dotted outline 39 shows an example of an alternate orientation of MLC 35.

A configuration of MLC 35 can be specified by a set of leaf positions that define a position of each leaf 36 and an orientation of MLC 35 about axis 37. The control system of a radiation delivery device (e.g. control system 23 of radiation delivery device 10) is typically capable of controlling the positions of leaves 36 and the orientation of MLC 35 about axis 37. MLCs can differ in design details, such as the number of leaves 36, the widths of leaves 36, the shapes of the ends and edges of leaves 36, the range of positions that any leaf 36 can have, constraints on the position of one leaf 36 imposed by the positions of other leaves 36, the mechanical design of the MLC, and the like. The invention described herein should be understood to accommodate any type of configurable beam-shaping apparatus 33 including MLCs having these and other design variations.

The configuration of MLC 35 may be changed (for example, by moving leaves 36 and/or rotating MLC 35 about axis 37) while radiation source 12 is operating and while radiation source 12 is moving about trajectory 30, thereby allowing the shape of aperture(s) 38 to be varied dynamically while radiation is being delivered to a target volume in subject S. Since MLC 35 can have a large number of leaves 36, each of leaves 36 can be placed in a large number of positions and MLC 35 can be rotated about its axis 37, MLC 35 may have a very large number of possible configurations.

FIG. 4A schematically depicts a method 50 according to an example embodiment of this invention. An objective of method 50 is to establish a radiation treatment plan that will deliver a desired radiation dose distribution to a target volume in a subject S (to within an acceptable tolerance), while minimizing the dose of radiation delivered to tissues surrounding the target volume or at least keeping the dose delivered to surrounding tissues below an acceptable threshold. This objective may be achieved by varying: (i) a cross-sectional shape of a radiation beam (e.g. beam 14); and (ii) an intensity of the radiation beam, while moving radiation source 12 and/or beam 14 along a trajectory 30 relative to subject S. In some embodiments, as discussed above, these objectives are achieved while radiation source 12 and/or beam 14 are caused to move continuously along trajectory 30.

Method 50 may be performed, at least in part, by a treatment planning system 25 (e.g. treatment planning system 25 of FIG. 1). In the illustrated embodiment, treatment planning system 25 comprises its own controller 25A which is configured to execute suitable software 25B. In other embodiments, control system 23 and treatment planning system 25 may share a controller. Controller 25 may comprise one or more data processors, together with suitable hardware, including, by way of non-limiting example: accessible memory, logic circuitry, drivers, amplifiers, A/D and D/A converters and like. Such a controller may comprise, without limitation, a microprocessor, a computer-on-a-chip, the CPU of a computer or any other suitable microcontroller. Controller 25 may comprise a plurality of data processors.

A desired amount of radiation dose to be delivered to the target volume (referred to as the “desired dose distribution”) and a suitable trajectory 30 may be defined in advance. Method 50 derives the shape that beam 14 ought to have during movement of source 12 and/or beam 14 along trajectory 30 and the intensity with which radiation ought to be delivered during movement of source 12 and/or beam 14 along trajectory 30. The shape of beam 14 may be determined by a suitable configuration of a beam-shaping mechanism 33, such as MLC 35.

In block 52, method 50 obtains a set of optimization goals 61 and trajectory data 62 defining a desired trajectory 30. Optimization goals 61 comprise dose distribution data 60, which defines a desired dose distribution, and may comprise other optimization goals 63. Optimization goals 61 and/or trajectory data 62 may have been developed by health professionals, such as a radiation oncologist in consultation with a radiation physicist, for example. Optimization goals 61 and/or trajectory data 62 may be specified by an operator as a part of block 52.

The person or persons who develop trajectory 30 may have reference to factors such as:

the condition to be treated;

the shape, size and location of the target volume;

the locations of critical structures that should be spared; and

other appropriate factors.

Trajectory 30 may be selected to minimize treatment time.

Radiation delivery apparatus according to some embodiments of the invention may provide one or more pre-defined trajectories. In such cases, block 52 may comprise selecting a pre-defined trajectory 30 or a template that partially defines a trajectory 30 and can be completed to fully define the trajectory 30.

As discussed above, optimization goals 61 comprise dose distribution data 60 and may comprise other optimization goals 63. Other optimization goals 63 may be specified by an operator as a part of block 52. By way of non-limiting example, other optimization goals 63 may comprise a desired uniformity of dose distribution in the target volume (or a desired precision with which the dose distribution in the target volume should match desired dose distribution data 60). Other optimization goals 63 may also define volumes occupied by important structures outside of the target volume and set limits on the radiation doses to be delivered to those structures. Other optimization goals 63 may define a maximum time required to deliver the radiation based on an individual patient's ability to stay still during treatment. For example, a child may be more likely to move during treatment than an adult and such movement may cause incorrect dose delivery. Consequently, it may be desirable to lower the maximum dose delivery time for the child to minimize the risk that the child may move during treatment. Other optimization goals 63 may also set priorities (weights) for different optimization goals.

Other optimization goals 63 may have any of a variety of different forms. For example, a biological model may be used in the computation of a metric which estimates a probability that a specified dose distribution will control a disease from which the subject is suffering and/or the probability that a specified dose delivered to non-diseased tissue may cause complications. Such biological models are known as radiobiological models. Other optimization goals 63 may be based in part on one or more radiobiological models. The physical limitations of a particular radiation delivery apparatus may also be taken into account as another example of an optimization goal 63. As mentioned above, gantry 12 can be relatively massive and controlled movement of gantry 12 may be difficult and may cause strain to various components of the radiation delivery apparatus. As a particular example, one optimization goal 63 may be to have gantry 16 move continuously (i.e. without stopping) over the specified trajectory 30.

Method 50 then proceeds to an optimization process 54, which seeks desirable beam shapes and intensities as a function of the position of source 12 and/or beam 14 along trajectory 30. In the illustrated embodiment of method 50, optimization process 54 involves iteratively selecting and modifying one or more optimization variables affecting the beam shape or the beam intensity. For example, the optimization variable(s) may comprise a position of a leaf 36 in a MLC 35 at a control point 32 (which determines a shape of beam 14), an orientation of MLC 35 about axis 37 at a control point 32 (which determines a shape of beam 14) and/or an intensity of beam 14 at a control point 32. The quality of the dose distribution resulting from the modified optimization variable(s) is evaluated in relation to a set of one or more optimization goals. The modification is then accepted or rejected. Optimization process 54 continues until it achieves an acceptable set of beam shapes and intensities or fails.

In the illustrated method 50, optimization process 54 begins in block 56 by establishing an optimization function. The block 56 optimization function is based, at least in part, on optimization goals 61. The set of optimization goals 61 includes the desired dose distribution data 60 and may include one or more other optimization goals 63. The block 56 optimization function may comprise a cost function. Higher costs (corresponding to circumstances which are farther from optimization goals 61) may be associated with factors such as:

-   -   deviations from the desired dose distribution data 60;     -   increases in the radiation dose delivered outside of the target         volume;     -   increases in the radiation dose delivered to critical structures         outside of the treatment volume;     -   increases in the time required to deliver the radiation         treatment; and/or     -   increases in the total radiation output required for the         delivery of the treatment.         Lower costs (corresponding to circumstances which are closer to         optimization goals 61) may be associated with factors such as:     -   radiation doses that come closer to matching specified         thresholds (which may be related to desired dose distribution         data 60);     -   no radiation doses exceeding specified thresholds;     -   reductions in radiation dose outside of the target volume;     -   reductions in radiation dose delivered to critical structures         outside of the target volume;     -   decreases in the time required to deliver the radiation         treatment; and/or     -   decreases in the total radiation output required for the         delivery of the treatment.         These factors may be weighted differently from one another.         Other factors may also be taken into account when establishing         the block 56 optimization function.

The result of block 56 is an optimization function which takes as input a dose distribution and produces an output having a value or values that indicate how closely the input dose distribution satisfies a set of optimization goals 61.

Block 58 involves initializing beam shapes and intensities for a number of control points 32 along trajectory 30. The initial beam shapes and intensities may be selected using any of a wide variety of techniques. Initial beam shapes may be selected by specifying a particular configuration of MLC 35. By way of non-limiting example, initial beam shapes specified in block 58 may be selected by any of:

-   -   setting the beam shape at each control point 32 along trajectory         30 to approximate a beam's eye view outline of the target volume         (taken from control point 32);     -   setting the beam shape so that radiation is blocked from healthy         tissue structures only;     -   initializing leaves 36 of MLC to be in a specified configuration         such as fully open, fully closed, half-open, or defining a shape         for aperture 38 (e.g. round, elliptical, rectangular or the         like); and     -   randomizing the positions of leaves 36 of MLC.         The particular way that the beam shapes are initialized is not         critical and is limited only by the beam-shaping mechanism 33 of         particular radiation delivery apparatus.

By way of non-limiting example, the initial beam intensities specified in block 58 may be selected by any of:

-   -   setting all intensities to zero;     -   setting all intensities to the same value; and     -   setting intensities to random values.

In some embodiments, the beam shapes are initialized in block 58 to shapes that match a projection of the target (e.g. to approximate a beam's eye view outline of the target volume from each control point 32 along trajectory 30) and the intensities are initialized in block 58 to all have the same value which may be set so that the mean dose in the target volume will equal a prescribed dose.

In block 64, method 50 involves simulating the dose distribution resulting from the initial beam shapes and initial beam intensities. Typically, the block 64 simulation comprises a simulated dose distribution computation which is discussed in more detail below. Method 50 then determines an initial optimization result in block 65. The block 65 determination of the initial optimization result may comprise evaluating the block 56 optimization function on the basis of the block 64 simulated dose distribution.

In block 66, method 50 alters the beam shapes and/or intensities at one or more control points 32. The block 66 alteration of beam shapes and/or intensities may be quasi-random. The block 66 alteration of beam shapes and/or intensities may be subject to constraints. For example, such constraints may prohibit impossible beam shapes and/or intensities and may set other restrictions on beam shapes, beam intensities and/or the rate of change of beam shapes and/or beam intensities. In each execution of block 66, the alteration of beam shapes and/or intensities may involve a single parameter variation or multiple parameter variations to beam shape parameter(s) and/or to beam intensity parameter(s). The block 66 alteration of beam shapes and/or intensities and may involve variation(s) of these parameter(s) at a single control point 32 or at multiple control points 32. Block 68 involves simulating a dose distribution that would be achieved if the block 66 altered beam shapes and/or intensities were used to provide a radiation treatment. Typically, the block 68 simulation comprises a simulated dose distribution computation which is discussed in more detail below.

In some embodiments, the block 66 alteration of beam shapes and/or intensities is not chosen randomly, but rather is selected to give priority to certain parameter(s) that have large impacts on dose distribution quality. “Dose distribution quality” may comprise a reflection of how closely a simulated dose distribution calculation meets optimization goals 61. For example, where the beam is shaped by a MLC 35, certain leaves 36 or positions of leaves 36 may be given priority for modification. This may be done by determining a priori which leaves of MLC 35 have the most impact on dose distribution quality. Such an a priori determination of particularly important MLC leaves may be based, for example, on a calculation of the relative contributions to the block 56 optimization function from each voxel in the target region and the surrounding tissue and by a projection of beam ray lines intersecting a particular voxel to the plane of MLC 35.

In block 70, method 50 determines a current optimization result. The block 70 determination may comprise evaluating the block 56 optimization function on the basis of the block 68 simulated dose distribution. In block 72, the current optimization result (determined in block 70) is compared to a previous optimization result and a decision is made whether to keep or discard the block 66 alteration. The first time that method 50 arrives at block 72, the previous optimization result may be the block 65 initial optimization result. The block 72 decision may involve:

-   -   (i) deciding to preserve the block 66 alteration (block 72 YES         output) if the current optimization result is closer to         optimization goals 61 than the previous optimization result; or     -   (ii) deciding to reject the block 66 alteration (block 72 NO         output) if the current optimization result is further from         optimization goals 61 than the previous optimization result.         Other optimization algorithms may make the block 72 decision as         to whether to keep or discard the block 66 alteration based on         rules associated with the particular optimization algorithm. For         example, such optimization algorithms may, in some instances,         allow preservation of the block 66 alteration (block 72 YES         output) if the current optimization result is further from the         optimization goals 61 than the previous optimization result.         Simulated annealing is an example of such an optimization         algorithm.

If block 72 determines that the block 66 alteration should be preserved (block 72 YES output), then method 50 proceeds to block 73, where the block 66 altered beam shapes and intensities are updated to be the current beam shapes and intensities. After updating the beam shapes and intensities in block 73, method 50 proceeds to block 74. If block 72 determines that the block 66 alteration should be rejected (block 72 NO output), then method 50 proceeds directly to block 74 (i.e. without adopting the block 66 alterations).

Block 74 involves a determination of whether applicable termination criteria have been met. If the termination criteria have been met (block 74 YES output), method 50 proceeds to block 75, where the current beam shapes and intensities are saved as an optimization result. After block 75, optimization process 54 terminates. On the other hand, if the termination criteria have not been met (block 74 NO output), method 50 loops back to perform another iteration of blocks 66 through 74.

By way of non-limiting example, block 74 termination criteria may include any one or more of:

-   -   successful achievement of optimization goals 61;     -   successive iterations not yielding optimization results that         approach optimization goals 61;     -   number of successful iterations of blocks 66 through 74 (where a         successful iteration is an iteration where the block 66         variation is kept in block 73 (i.e. block 72 YES output));     -   operator termination of the optimization process.

The illustrated method 50 represents a very simple optimization process 54. Optimization process 54 may additionally or alternatively include other known optimization techniques such as:

simulated annealing;

gradient-based techniques;

genetic algorithms;

applying neural networks; or

the like.

Method 50 may be used as a part of an overall method for planning and delivering radiation dose to a subject S. FIG. 4B schematically depicts a method 300 for planning and delivering radiation dose to a subject S according to a particular embodiment of the invention. Method 300 begins in block 310, which, in the illustrated embodiment, involves obtaining a desired trajectory 30 and desired optimization goals 61. Method 300 then proceeds to block 320 which involves optimizing a set of radiation delivery parameters. In one particular embodiment, the block 320 optimization process may comprise an optimization of the beam shape and beam intensity parameters in accordance with optimization process 54 of method 50. The result of the block 320 optimization process is a radiation delivery plan. In block 330, the radiation delivery plan is provided to the control system of a radiation delivery apparatus (e.g. control system 23 of radiation delivery device 10 (FIG. 1)). In block 340, the radiation delivery apparatus delivers the radiation to a subject in accordance with the radiation treatment plan developed in block 320.

Method 50 involves the simulation of dose distribution that results from a particular set of beam shapes, beam intensities and motion axis positions (e.g. in blocks 64 and 68). Simulation of the dose distribution may be performed in any suitable manner. Some examples of dose calculation methods that may be employed to simulate dose distribution results comprise:

pencil beam superposition;

collapsed cone convolution; and

Monte Carlo simulation.

In some embodiments, the dose that would be delivered by a treatment plan is simulated (as in blocks 64 and 68 of method 50) by adding a contribution to the dose from each control point 32. At each of control points 32, the following information is known:

-   -   a position of source 12 and an orientation of beam 14 relative         to subject S including the target volume (as determined by the         positions of the available motion axes);     -   a beam shape (as determined, for example, by a rotation angle         and/or a configuration of the leaves 36 of a MLC 35); and     -   a beam intensity.

In some embodiments, the contribution to the dose at each control point 32 is determined by pencil beam superposition. Pencil beam superposition involves conceptually dividing the projected area of beam 14 into many small beams known as “beamlets” or “pencil beams”. This may be done by dividing a cross-sectional beam shape (e.g. aperture 38 of MLC 35) into a grid of square beamlets. The contribution to an overall dose distribution from a particular control point 32 may be determined by summing the contributions of the beamlets. The contribution to a dose distribution by individual beamlets may be computed in advance. Such contributions typically take into account radiation scattering and other effects that can result in the radiation from one beamlet contributing to dose in regions that are outside of the beamlet. In a typical MLC 35, there is some transmission of radiation through leaves 36. Consequently, when performing a dose simulation calculation, it is often desirable add some smaller contribution to the dose from outside of the beam shaping aperture 38 to account for transmission through leaves 36 of MLC 35.

FIG. 5A shows an aperture 38 of an MLC 35 divided into a plurality of beamlets 80. In general, it is desirable for beamlets 80 to be fairly small to permit precise modelling of the wide range of configurations that aperture 38 may have. Beamlets 80 may be smaller than the widths of the leaves 36 (not shown in FIG. 5A) of MLC 35. In FIG. 5A, 105 beamlets 80 are required to cover aperture 38 and, consequently, for a particular control point 32 having the aperture configuration shown in FIG. 5A, a dose simulation calculation (e.g. a portion of the block 68 dose simulation) involves a superposition of the dose contributed by 105 beamlets 80.

Some embodiments achieve efficiencies in this dose simulation computation by providing composite beamlets 82 that are larger than beamlets 80. A range of composite beamlets 82 having different sizes, shapes and/or orientations may be provided. FIG. 5B shows a number of composite beamlets 82A, 82B, 82C (collectively, beamlets 82) having different sizes and shapes. It can be seen from FIG. 5B, that composite beamlets 82 can be used in the place of a plurality of conventionally sized beamlets 80. An example application of composite beamlets 82 is shown in FIG. 5C. For a given shape of aperture 38, composite beamlets 82 are used in place of some or all of smaller beamlets 80. In the particular configuration of aperture 38 of FIG. 5C (which is the same as the configuration of aperture 38 of FIG. 5A), the area of aperture 38 is covered by 28 composite beamlets 82 (24 82A, one 84B, three 84C) and one smaller beamlet 80. Consequently, for a particular control point 32 having the aperture configuration of FIG. 5B, a dose simulation calculation (e.g. a portion of the block 68 dose simulation) is reduced to a superposition of the dose contributed by 29 beamlets 82, 80. Dose contributed by composite beamlets 82 may be determined in advance in a manner similar to the advance dose contribution from conventional beamlets 80.

The size and shape of composite beamlets 82 may be selected to reduce, and preferably minimize, the number of beamlets required to cover the area of aperture 38. This can significantly reduce calculation time without significantly reducing the accuracy of dose simulation. The use of composite beamlets is not limited to pencil beam superposition and may be used in other dose simulation calculation algorithms, such as Monte Carlo dose simulation and collapsed cone convolution dose simulation, for example.

The use of composite beamlets 82 to perform a dose simulation calculation assumes that there are only small changes in the characteristics of the tissue over the cross-sectional dimension of the composite beamlet 82. As composite beamlets are made larger, this assumption may not necessarily hold. Accordingly, the upper size limit of composite beamlets 82 is limited by the necessary calculation accuracy. In some embodiments, at least one dimension of composite beamlets 82 is greater than the largest dimension of conventional beamlet 80. In some embodiments, the maximum dimension of composite beamlets 82 is less than 25 times the size of the largest dimension of conventional beamlet 80.

The dose simulation computation (e.g. the block 68 dose simulation) is performed at a number of control points 32. Based on calculations for those control points 32, an estimated dose distribution is generated for a radiation source 12 that may be continuously moving over a trajectory 30 and continuously emitting a radiation beam 14, where the radiation beam 14 may have a continuously varying shape and intensity. Where a dose distribution is computed by summing contributions from discrete control points 32, the accuracy with which the computed dose will match the actual dose delivered by continuous variation of the position of source 12, the orientation of beam 14, the beam shape and the beam intensity will depend in part upon the number of control points 32 used to perform the dose simulation computation. If there are only a few control points 32, then it may not be possible to obtain accurate estimates of the delivered dose. The dose delivered by source 12 over a continuous trajectory 30 can be perfectly modelled by summing contributions from discrete control points 32 only at the limit where the number of control points 32 approaches infinity. Discretization of the dose simulation calculation using a finite number of control points 32 will therefore degrade the accuracy of the modelled dose distribution.

This concept is graphically illustrated in FIG. 6, which plots the dose simulation error against the number of control points 32. FIG. 6 clearly shows that where the dose simulation computation makes use of a large number of control points 32, the resultant error (i.e. the difference between simulation dose distribution and actual dose distribution) is minimized.

In some embodiments of the invention, constraints are imposed on the optimization process (e.g. block 54 of method 50). Such constraints may be used to help maintain the accuracy of the discretized dose simulation calculation to within a given tolerance. In some embodiments, these optimization constraints are related to the amount of change in one or more parameters that may be permitted between successive control points 32. Examples of suitable constraints include:

-   -   Radiation source 12 cannot travel further than a maximum         distance between consecutive control points 32. This may be         achieved entirely, or in part, by imposing a maximum change in         any motion axis between consecutive control points 32. Separate         constraints may be provided for each motion axis. For example, a         maximum angular change may be specified for gantry angle,         maximum changes in displacement may be provided for couch         translation etc.     -   Parameters affecting beam shape cannot change by more than         specified amounts between consecutive control points 32. For         example, maximum values may be specified for changes in the         positions of leaves 36 of a MLC 35 or changes in the rotation         orientation of MLC 35.     -   Parameters affecting beam shape cannot change by more than a         specified amount per unit of motion axis change. For example,         maximum values may be specified for changes in the positions of         leaves 36 of a MLC 35 for each degree of rotation of gantry 16         about axis 18.     -   The source intensity cannot change by more than a specified         amount between control points 32.     -   The source intensity cannot change by more that a specified         amount per unit of motion axis change.     -   The source intensity cannot exceed a certain level.         It will be appreciated that where a dose simulation calculation         is based on a number of discretized control points, constraints         which force small changes of motion axes parameters, beam shape         parameters and/or beam intensity parameters between control         points can produce more accurate dose simulation calculations.

In addition to improving the accuracy of the dose simulation calculation, the imposition of constraints may also help to reduce total treatment time by accounting for the physical limitations of particular radiation delivery apparatus. For example, if a particular radiation delivery apparatus has a maximum radiation output rate and the optimization solution generated by method 50 involves a radiation intensity that results in a radiation output rate higher than this maximum radiation output rate, then the rate of movement of the motion axes of the radiation delivery apparatus will have to slow down in order to deliver the intensity prescribed by the block 54 optimization process. Accordingly, a constraint imposed on the maximum source intensity during the block 54 optimization can force a solution where the prescribed intensity is within the capability of the radiation delivery apparatus and the motion axes of the radiation delivery apparatus do not have to slow down. Since the motion axes do not have to slow down, such a solution can be delivered to subject S relatively quickly, causing a corresponding reduction in total treatment time. Those skilled in the art will appreciate that other constraints may be used to account for other limitations of particular radiation delivery apparatus and can be used to reduce total treatment time.

An example of how such constraints may be defined is “For an estimated dose to be within 2% of the actual dose distribution, the following parameters should not change by more than the stated amounts between any two consecutive control points 32:

intensity—10%;

MLC leaf position—5 mm;

MLC orientation—5%;

gantry angle—1 degree; and

couch position—3 mm.”

The number of control points 32 used in optimization process 54 also impacts the number of iterations (and the corresponding time) required to implement optimization process 54 as well as the quality of the dose distribution. FIG. 7 graphically depicts the dose distribution quality as a function of the number of iterations involved in a block 54 optimization process for various numbers of control points 32.

FIG. 7 shows plots for 10 control points, 50 control points, 100 control points and 300 control points on a logarithmic scale. It will be appreciated by those skilled in the art that the number of iterations (the abscissa in FIG. 7) is positively correlated with the time associated to perform the optimization. FIG. 7 shows that when the number of control points 32 is relatively low, the quality of the dose distribution improves rapidly (i.e. over a relatively small number of iterations). However, when the number of control points 32 is relatively low, the quality of the resultant dose distribution is relatively poor and, in the cases of 10 control points and 50 control points, the quality of the dose distribution does not achieve the optimization goals 61. Conversely, if a relatively large number of control points 32 is used, the block 54 optimization requires a relatively large number of iterations, but the quality of the dose distribution eventually achieved is relatively high and exceeds the optimization goals 61. In some cases, where the number of control points 32 is relatively high, the number of iterations required to achieve a solution that meets the optimization goals 61 can be prohibitive (i.e. such a solution can take too long or can be too computationally expensive).

The impact of the number of control points 32 on the block 54 optimization process may be summarized as follows. If a relatively small number of control points 32 are used:

-   -   there may be relatively large changes in the motion axes         parameters (i.e. beam position and beam orientation), the beam         shape parameters (e.g. positions of leaves 36 of MLC 35 and/or         the orientation of MLC 35) and beam intensity between control         points 32 (i.e. the constraints on the motion axes parameters,         the beam shape parameters and the beam intensity will be         relatively relaxed as between control points 32);     -   because of the relatively relaxed constraints and the large         range of permissible changes to the beam shape and intensity         parameters, it is possible to explore a relatively large range         of possible configurations of the beam intensity and beam shape         during optimization process 54;     -   because of the ability to explore a relatively large range of         possible beam shape and intensity configurations, the block 54         optimization process will tend to approach the optimization         goals 61 after a relatively small number of iterations;     -   because there are fewer control points available at which the         beam shape parameters and/or beam intensity parameters may be         varied, it may be difficult or impossible for the block 54         optimization process to derive a dose distribution that meets or         exceeds optimization goals 61; and     -   the accuracy of dose simulation computations based on the         relatively small number of control points 32 will be relatively         poor and may be outside of an acceptable range.

If a relatively large number of control points 32 are used:

-   -   the possible magnitudes of the changes in the motion axes         parameters (i.e. beam position and beam orientation), the beam         shape parameters (e.g. positions of leaves 36 of MLC 35 and/or         orientation of MLC 35) and beam intensity between control points         32 are relatively low (i.e. the constraints on the motion axes         parameters, the beam shape parameters and the beam intensity         will be relatively restrictive as between control points 32);     -   because of the relatively restrictive constraints and the small         range of permissible changes to the beam shape and intensity         parameters, only a relatively small range of possible beam shape         and beam intensity configurations may be explored during         optimization process 54;     -   because of the limited range of possible beam shape and         intensity configurations, it may take a relatively large number         of iterations for the block 54 optimization process to approach         the optimization goals 61;     -   because there are more control points available at which the         beam shape and/or the beam intensity may be varied, it may be         easier to derive a dose distribution that meets or exceeds         optimization goals 61; and     -   the accuracy of dose simulation computations based on the         relatively large number of control points 32 will be relatively         good.

In some embodiments, the benefits of having a small number of control points 32 and the benefits of having a large number of control points 32 are achieved by starting the optimization process with a relatively small number of control points 32 and then, after a number of initial iterations, inserting additional control points 32 into the optimization process. This process is schematically depicted in FIG. 8.

FIG. 8 shows a method 150 of optimizing dose delivery according to another embodiment of the invention. Method 150 of FIG. 8 may be used as a part of block 320 in method 300 of FIG. 4B. In many respects, method 150 of FIG. 8 is similar to method 50 of FIG. 4A. Method 150 comprises a number of functional blocks which are similar to those of method 50 and which are provided with reference numerals similar to the corresponding blocks of method 50, except that the reference numerals of method 150 are proceeded by the numeral “1”. Like method 50, the objective of method 150 is to establish a radiation treatment plan that will deliver a desired radiation dose distribution to a target volume in a subject S (to within an acceptable tolerance), while minimizing the dose of radiation delivered to tissues surrounding the target volume or at least keeping the dose delivered to surrounding tissues below an acceptable threshold. This objective may be achieved by varying: (i) a cross-sectional shape of radiation beam 14; and (ii) an intensity of beam 14, while moving radiation source 12 and/or beam 14 along a trajectory 30 relative to subject S.

The principal difference between method 50 of FIG. 4A and method 150 of FIG. 8 is that the optimization process 154 of method 150 involves a repetition of the optimization process over a number of levels. Each level is associated with a corresponding number of control points 32 and the number of control points 32 increases with each successive level. In the illustrated embodiment, the total number of levels used to perform the block 154 optimization (or, equivalently, the final number of control points 32 at the conclusion of the block 154 optimization process) is determined prior to commencing method 150. For example, the final number of control points 32 may be specified by an operator depending, for example, on available time requirements, accuracy requirements and/or dose quality requirements. In other embodiments, depending on termination conditions explained in more detail below, the final number of control points 32 may vary for each implementation of method 150.

Method 150 starts in block 152 and proceeds in the same manner as method 50 until block 158. In the illustrated embodiment, block 158 differs from block 58 in that block 158 involves the additional initialization of a level counter. In other respects, block 158 is similar to block 58 of method 50. Initialization of the level counter may set the level counter to 1 for example. When the level counter is set to 1, method 150 selects a corresponding level 1 number of control points 32 to begin the block 154 optimization process. The level 1 number of control points 32 is preferably a relatively low number of control points. In some embodiments, the level 1 number of control points 32 is in a range of 2-50. As discussed in more detail below, the level counter is incremented during the implementation of method 150 and each time the level counter is incremented, the corresponding number of control points 32 is increased.

Using a number of control points 32 dictated by the level counter, method 150 proceeds with blocks 164 through 174 in a manner similar to blocks 64 through 74 of method 50 discussed above. Block 174 differs from block 74 in that block 174 involves an inquiry into the termination conditions for a particular level of method 150. The termination conditions for a particular level of method 150 may be similar to the termination conditions in block 74 of method 50. By way of non-limiting example, the termination conditions for block 174 may comprise any one or more of:

-   -   successful achievement of optimization goals 61 to within a         tolerance level which may be particular to the current level;     -   successive iterations not yielding optimization results that         approach optimization goals 61; and     -   operator termination of the optimization process.         Additionally or alternatively, the block 174 termination         conditions may include reaching a maximum number of iterations         of blocks 166 through 174 within a particular level of method         150 regardless of the resultant optimization quality. For         example, the maximum number of iterations for level 1 may be         10⁴. The maximum number iterations may vary for each level. For         example, the maximum number of iterations may increase for each         level in conjunction with a corresponding increase in the number         of control points 32 or may decrease for each level in         conjunction with a corresponding increase in the number of         control points 32.

Additionally or alternatively, the block 174 termination conditions may include reaching a maximum number of successful iterations of blocks 166 through 174 within a particular level of method 150 (i.e. iterations where method 150 proceeds through the block 172 YES output and the block 166 variation is kept in block 173). Again, the maximum number of successful iterations may vary (increase or decrease) for each level. In some embodiments, the maximum number of successful iterations within a particular level decreases as the level (i.e. the number of control points 32) increases. In one particular embodiment, the maximum number of successful iterations decreases exponentially as the level increases.

If the termination criteria have not been met (block 174 NO output), method 150 loops back to perform another iteration of blocks 166 through 174 at the current level. If the termination criteria have been met (block 174 YES output), method 150 proceeds to block 178, where method 150 inquires into the general termination conditions for optimization process 154. The general termination conditions of block 178 may be similar to the termination conditions in block 174, except the block 178 termination conditions pertain to optimization process 154 as a whole rather than to a particular level of optimization process 154. By way of non-limiting example, the termination conditions for block 178 may comprise any one or more of:

-   -   successful achievement of optimization goals 61 to within a         tolerance level particular to optimization process 154 as a         whole;     -   successive iterations not yielding optimization results that         approach optimization goals 61; and     -   operator termination of the optimization process.         Additionally or alternatively, the block 178 termination         conditions may include reaching a suitable minimum number of         control points 32. This minimum number of control points may         depend on the number of control points 32 required to ensure         that dose simulation calculations have sufficient accuracy (see         FIG. 6).

The block 178 termination conditions may additionally or alternatively comprise having minimum threshold level(s) of control points 32 for corresponding changes in the motion axes parameters, the beam shape parameters and/or the beam intensity parameter. In one particular example, the block 178 termination conditions may comprise minimum threshold level(s) of at least one control point 32 for:

each intensity change greater than 10%;

each MLC leaf position change greater than 5 mm;

each MLC orientation change greater than 5°;

each gantry angle change greater than 1°; and/or

each couch position change greater than −3 mm.

If the block 178 termination criteria have been met (block 178 YES output), method 150 proceeds to block 175, where the current beam shapes and intensities are saved as an optimization result. After block 175, method 150 terminates. On the other hand, if the block 178 termination criteria have not been met (block 178 NO output), method 150 proceeds to block 180, where the number of control points 32 is increased.

The addition of new control points 32 in block 180 may occur using a wide variety of techniques. In one particular embodiment, new control points 32 are added between pairs of existing control points 32. In addition to adding new control points 32, block 180 comprises initializing the parameter values associated with the newly added control points 32. For each newly added control point 32, such initialized parameter values may include: motion axes parameters which specify the position of source 12 and the orientation of beam 14 (i.e. the set of motion axis positions corresponding to the newly added control point 32); an initial beam shape parameter (e.g. the configuration of the leaves 36 and/or orientation of a MLC 35); and an initial beam intensity parameter.

The motion axes parameters corresponding to each newly added control point 32 may be determined by the previously specified trajectory 30 (e.g. by desired trajectory data 62). The initial beam shape parameters and the initial beam intensity parameters corresponding to each newly added control point 32 may be determined by interpolating between the current beam shape parameters and current beam intensity parameters for previously existing control points 32 on either side of the newly added control point 32. Such interpolation may comprise linear or non-linear interpolation for example.

The initial parameter values for the newly added control points 32 and the subsequent permissible variations of the parameter values for the newly added control points 32 may be subject to the same types of constraints discussed above for the original control points 32. For example, the constraints on the parameter values for newly added control points 32 may include:

-   -   constraints on the amount that radiation source 12 (or any one         or more motion axes) can move between control points 32;     -   constraints on the amount that the beam shape can change between         successive control points 32 (e.g. constraints on the maximum         rotation of MLC 35 or movement of the leaves 36 of MLC 35); or     -   constraints on the amount that the intensity of source 12 may         change between successive control points 32.         Those skilled in the art will appreciate that the magnitude of         these optimization constraints will vary with the number of         control points 32 and/or the separation of adjacent control         points 32. For example, if the constraint on a maximum movement         of a leaf 36 of MLC 35 is 2 cm between successive control points         32 when there are 100 control points 32 and the number of         control points 32 is doubled to 200, the constraint may be         halved, so that the constraint on the maximum movement of a leaf         36 of MLC 35 is 1 cm between control points 32 (assuming that         the newly added control points 32 are located halfway between         the existing control points 32).

After adding and initializing the new control points 32 in block 180, method 180 proceeds to block 182 where the level counter 182 is incremented. Method 150 then returns to block 164, where the iteration process of blocks 164 through 174 is repeated for the next level.

An example of the method 150 results are shown in FIG. 9, which graphically depicts the dose distribution quality versus the number of iterations on a linear scale. FIG. 9 also shows that the number of control points 32 increases as the dose distribution gets closer to the optimization goals 61. It can be seen that by starting the optimization process with a relatively low number of control points 32 and then adding additional control points 32 as the optimization process approaches the optimization goals 61, the number of iterations required to achieve an acceptable solution has been dramatically reduced. FIG. 9 also shows that:

-   -   the use of a small number of control points 32 at the beginning         of the optimization process allows the optimization to get close         to optimization goals 61 after a relatively small number of         iterations;     -   the introduction of additional control points 32 during the         course of the optimization allows the flexibility to derive a         dose distribution that meets optimization goals 61; and     -   before the overall optimization process is terminated, a large         number of control points 32 have been added and the parameters         associated with these additional control points obey the         associated optimization constraints, thereby preserving the dose         calculation accuracy.

As with method 50 discussed above, method 150 describes a simple optimization process 154. In other embodiments, the block 154 optimization process may additionally or alternatively include other known optimization techniques such as: simulated annealing, gradient-based techniques, genetic algorithms, applying neural networks or the like.

In method 150, additional control points 32 are added when the level is incremented. In a different embodiment, the addition of one or more new control points may be treated as an alteration in block 66 of method 50. In such an embodiment, the procedures of block 180 associated with the addition of control points 32 may be performed as a part of block 66. In such an embodiment, the termination conditions of block 74 may also comprise an inquiry into whether the optimization has achieved a minimum number of control points 32. In other respects, such an embodiment is similar to method 50.

The result of optimization method 50 or optimization method 150 is a set of control points 32 and, for each control point 32, a corresponding set of parameters which includes: motion axes parameters (e.g. a set of motion axis positions for a particular radiation delivery apparatus that specify a corresponding beam position and beam orientation); beam shape parameters (e.g. a configuration of an MLC 35 including a set of positions for leaves 36 and, optionally, an orientation of MLC 35 about axis 37); and a beam intensity parameter. The set of control points 32 and their associated parameters are then transferred to a radiation delivery apparatus to effect the dose delivery.

A control system of the radiation delivery apparatus (e.g. control system 23 of radiation delivery apparatus 10) uses the set of control points 32 and their associated parameters to move radiation source 12 over a trajectory 30 while delivering radiation dose to a subject S. While the radiation delivery apparatus is moving over trajectory 30, the control system controls the speed and/or position of the motion axes, the shape of the beam and the beam intensity to reflect the motion axis parameters, beam shape parameters and the beam intensity parameters generated by the optimization methods 50, 150. It will be appreciated by those skilled in the art that the output of the optimization methods 50, 150 described above may be used on a wide variety of radiation delivery apparatus.

Pseudocode for Exemplary Embodiment of Optimization Process

Pre-Optimization

-   -   Define 3-dimensional target and healthy tissue structures.     -   Set optimization goals for all structures based on one or more         of:         -   Histograms of cumulative dose;         -   Prescribed dose required to the target;         -   Uniformity of dose to the target;         -   Minimal dose to healthy tissue structures.     -   Combine all optimization goals into a single quality factor         (i.e. an optimization function).     -   Define the trajectory for the radiation source:         -   Select a finite number of control points; and         -   Set the axis position for each axis at each control point.

Initialization

-   -   Configure MLC characteristics (e.g. leaf width, transmission).     -   Initialize level counter and initial number of control points.     -   Initialize MLC leaf positions to shape the beam to the outline         of the target.     -   Perform dose simulation calculation to simulate dose         distribution for all targets and healthy tissue structures:         -   Generate a random distribution of points in each             target/structure;         -   Calculate the dose contribution from each initial control             point; and         -   Add the contribution from each initial control point.     -   Rescale the beam intensity and corresponding dose so that the         mean dose to the target is the prescription dose.     -   Set constraints for:         -   maximum change in beam shape parameters (i.e. movement of             MLC leaves and/or rotations of MLC); and         -   maximum change in beam intensity;     -   for corresponding variations the relevant motor axes, including,         where relevant:         -   Gantry angle;         -   Couch angle;         -   Couch position; and         -   MLC angle.     -   Set maximum intensity constraint.     -   Set maximum treatment time constraint.     -   Set optimization parameters:         -   Probability of adding control points;         -   At each iteration:             -   Probability of changing beam shape parameter (e.g. MLC                 leaf position or MLC orientation) taking into account                 constraints on range of changes in MLC leaf position;                 and             -   Probability of changing a radiation intensity taking                 into account constraints on range of intensity changes.

Optimization

While the optimization goals have not been attained: 1. Select a control point. 2. Select a beam shape alteration, intensity alteration, or add control points.

-   -   If a beam shape alteration (e.g. a change in position of an MLC         leaf) is selected:         -   Randomly select an MLC leaf to change;         -   Randomly select a new MLC leaf position;         -   Ensure that the new MLC leaf position does not violate any             positional constraints:             -   Leaf does not overlap with opposing leaf;             -   Leaf does not move outside of the initialized aperture;                 and             -   Leaf does not violate the maximum movement constraints.         -   Perform dose distribution simulation to calculate the new             dose distribution for all structures.         -   Calculate quality factor (i.e. optimization function) for             new dose distribution.         -   If the quality factor (i.e. optimization function) indicates             an improvement, then accept the new leaf position.     -   If an intensity alteration is selected:         -   Randomly select a new intensity;         -   Ensure that the new intensity does not violate any             constraints:             -   Intensity cannot be negative;             -   Intensity cannot violate the maximum intensity                 constraint; and             -   Intensity cannot violate the maximum intensity variation                 constraints.         -   Perform dose distribution simulation to calculate the new             dose distribution for all structures.         -   Calculate quality factor (i.e. optimization function) for             new dose distribution.         -   If the quality factor (i.e. optimization function) indicates             an improvement, then accept the new intensity.     -   If adding control points is selected:         -   Insert one or more control points within the existing             trajectory.         -   Adjust optimization constraints (e.g. beam shape constraints             and intensity constraints) based on addition of new control             points.         -   Initialize beam shape parameters, intensity parameters and             motion axes parameters of new control point(s).         -   Perform dose distribution simulation (incorporating the new             control points) to calculate the new dose distribution for             all structures.         -   Rescale all intensities so that the new intensities provide             a mean dose to the target equal to the prescription dose.         -   Continue optimization with the added control points.     -   If the termination criteria have been attained:         -   Terminate the optimization; and         -   Record all optimized parameters (e.g. beam shape parameters,             motion axes parameters and beam intensity parameters) and             transfer optimized parameters to the radiation device.     -   If the termination criteria has not be attained:         -   Go to step (1) and select another beam shape alteration,             intensity alteration, or add control points.

EXAMPLE IMPLEMENTATION OF A PARTICULAR EMBODIMENT

The following represents an illustrative example implementation of a particular embodiment of the invention. FIG. 10 shows a three-dimensional example of target tissue 200 and healthy tissue 202 located within the body of a subject S. This example simulates a radiation delivery apparatus similar to radiation delivery apparatus 10 (FIG. 1).

In this example, a trajectory 30 is defined as a 360° rotation of gantry 16 about axis 18 and a movement of couch 15 in the −Z direction (as shown in the coordinate system of FIG. 10). While this particular example uses a trajectory 30 involving two motion axes, it will be appreciated that trajectory 30 may involve movement of fewer motion axes or a greater number of motion axes. FIGS. 11A and 11B respectively depict the initial control point 32 positions of the relevant motion axes corresponding to the selected trajectory 30 (i.e. the angular positions of gantry 16 about axis 18 and the position of couch 15 in the Z dimension).

For this example, the optimization goals 61 included a desired dose distribution 60 having a uniform level of 70 Gy for target 200 and a maximum dose of 35 Gy for healthy tissue 202. At each initial control point 32, the beam shape parameters were initialized such that the leaves 36 of a MLC 35 shaped the beam into a beam's eye view outline of target 200. In this example, the orientation of MLC 35 was maintained constant at 45°. At each initial control point 32, the beam intensity was initialized so that the mean dose delivered to the target 200 was 70 Gy.

FIGS. 12A-F graphically depict the simulated dose distribution calculation at various stages of the optimization process by way of a dose volume histogram (DVH). In FIGS. 12A-F, dashed line 204 represents the percentage of the volume of healthy tissue 202 that receives a certain quantity of dose and the solid line 206 represents the percentage of the volume of target 200 that receives a certain quantity of dose. A DVH is a convenient graphical tool for evaluating dose distribution quality. It will be appreciated that movement of dashed line 204 downwardly and leftwardly represents a minimization of dose delivered to healthy tissue 202 and that movement of solid line 206 upwardly (as far as 100%) and rightwardly (as far as the dose distribution target (70 Gy in this example)) represents effective delivery of dose to target 200.

In this example, the optimization process starts at zero iterations with the 12 control points depicted in FIGS. 11A and 11B. The result at zero iterations is shown in FIG. 12A. In this example, the number of iterations and the number of control points are increased during the optimization process as shown in FIG. 12B-12F. After 900 iterations and an increased to 23 control points (FIG. 12B), a dramatic improvement in dose quality can be observed by the leftwardly and downwardly movement of dashed line 204. Further improvement is seen at 1800 iterations and 45 control points (FIG. 12C) and at 3200 iterations and 89 control points (FIG. 12D). The magnitude of the improvement in dose distribution quality per iteration decreases as the optimization progresses. FIGS. 12D-12F show that there is little improvement in the dose distribution quality between 3200 iterations and 89 control points (FIG. 12D), 5800 iterations and 177 control points (FIG. 12E) and 8500 iterations and 353 control points. As discussed above, notwithstanding the minimal improvement in dose distribution quality between FIGS. 12D and 12F, it can be useful to continue to increase the number of control points in the optimization to improve the accuracy of the dose simulation calculations.

FIG. 13 is another graphical representation of this example which shows how the optimization goals 61 are achieved (to within an acceptable tolerance level) after 5800 iterations (177 control points).

The optimization of this example was terminated after 11,000 iterations because the optimization goals had been attained (to within acceptable tolerances) and there was no further improvement in the dose distribution quality or accuracy with further iterations. The results of this example are shown in FIGS. 14A-14D, which respectively depict the motion axes parameters at each of the final control points (in this case, the orientation of gantry 16 about axis 18 (FIG. 14A) and the Z position of couch 15 (FIG. 14B)), the radiation intensity at each of the final control points (FIG. 14C) and the beam shaping parameters at each of the final control points (in this case, positions of two leaves 36 of an MLC 35 (FIG. 14D)). FIG. 14D shows that there are no dramatic changes in position of the illustrated leaves 36 of MLC 3, as constraints were applied to the allowable rate of change of the leaves 36 of MLC 35.

FIG. 15 shows a two-dimensional cross-section of the optimized dose distribution. FIG. 15 shows plots contour lines of constant dose (isodose lines) indicating the regions of high and low dose. The amount of dose associated with each isodose line is enumerated on the line itself. Recalling the shape and relative position of the target 200 and healthy tissue 202 from FIG. 10, FIG. 15 shows that the high dose region is confined to the c-shape target area 200 while inside the concavity (i.e. the region of healthy tissue 202), the dose is significantly reduced.

In this example, the optimization time was 15.3 minutes. The treatment time required to deliver this dose distribution is approximately 1.7 minutes (assuming a dose rate of 600 MU/min).

In some embodiments, the methods described herein for delivering radiation dose to a subject S are used in conjunction with one or more imaging techniques and corresponding imaging apparatus. A suitable imaging technique is cone-beam computed tomography (cone-beam CT), which obtains a three-dimensional image of a subject. Cone-beam CT involves a radiation source and a corresponding sensor which can be suitably mounted on a radiation delivery apparatus. For example, a cone-beam CT radiation source may be mounted on gantry 16 of radiation delivery apparatus 10 and a corresponding sensor may be mounted on the opposing side of subject S to detect radiation transmitted through subject S. In some embodiments, the cone-beam CT source is the same as the treatment radiation source 12. In other embodiments, the cone-beam CT source is different than the treatment radiation source 12. The radiation delivery apparatus may move the cone-beam CT source and the CT sensor relative to subject S using the same motion axes (or substantially similar motion axes) used to move the treatment radiation source 12. At any point in which the cone-beam CT source is activated, a 2-dimensional projection image is formed from the transmission of radiation emanating from the cone-beam CT source, passing through subject S and impinging onto the corresponding sensor (which typically comprises a 2-dimensional array of radiation sensors). In some embodiments, the cone-beam CT radiation source and the treatment radiation source are time division multiplexed, such that the cone-beam CT sensor can distinguish between imaging radiation and treatment radiation.

In the acquisition of a 3-dimensional cone-beam CT image, the cone-beam CT source and sensor array move through a trajectory to acquire a plurality of 2-dimensional projection images of subject S. The plurality of 2-dimensional projection images are combined using methods known to those skilled in the art in order to reconstruct the 3-dimensional image of subject S. The 3-dimensional image may contain spatial information of the target and healthy tissue.

In some embodiments, a cone-beam CT image of subject S is acquired while delivering radiation to the subject. The 2-dimensional images may be taken from around the same trajectory 30 and in the same time interval that the radiation is delivered to subject S. In such embodiments, the resultant cone-beam CT image will be representative of the subject position, including the 3-dimensional spatial distribution of target and healthy tissue, at the time the subject was treated. The spatial distribution of target and healthy tissue can be referenced to the particular radiation delivery apparatus, allowing an observer to accurately assess what radiation dose distribution was actually delivered to the target and healthy tissue structures.

Subject S, and more particularly, the locations of target and healthy tissue, can move during radiation delivery. While some movement can be reduced or eliminated, one difficult movement to stop is respiration. For example, when subject S breathes, a target located inside the lung may shift as a function of the breathing cycle. In most dose simulation calculations, subject S is assumed to be stationary throughout the delivery. Accordingly, ordinary breathing by subject S can result in incorrect delivery of dose to the target and healthy tissue. In some embodiments, radiation source 12 is activated only when a position or configuration of subject S is within a specified range.

In some embodiments, one or more sensors are used to monitor the position of subject S. By way of non-limiting example, such sensors may include respirometer, infrared position sensors, electromyogram (EMG) sensors or the like. When the sensor(s) indicate that subject S is in an acceptable position range, radiation source 12 is activated, the configuration of beam-shaping mechanism 33 changes and the motion axes move as described in the radiation treatment plan. When the sensor(s) indicate that subject S is not in the acceptable position range, the radiation is deactivated, the configuration of beam-shaping mechanism 33 is fixed and the motion axes are stationary. An acceptable position range may be defined as a particular portion of the respiratory cycle of subject S. In such embodiments, the radiation treatment plan is delivered intermittently, with intervals where the radiation apparatus and radiation output are paused (i.e. when the subject is out of the acceptable position range) and intervals where the radiation apparatus and radiation output are resumed (i.e. when the subject is in the acceptable position range). Treatment delivery proceeds in this way until the treatment plan has been completely delivered. The process of position dependent delivery of radiation may be referred to as “position gating” of radiation delivery.

In one particular embodiment of the invention, cone-beam CT images are acquired while position gated treatment is being delivered to subject S. The acquisition of 2-dimensional projection images may also gated to the patient position, so that the cone-beam CT images will represent the position of subject S at the time of treatment delivery. Such embodiments have the additional benefit that the 2-dimensional cone-beam CT images are obtained with subject S in a consistent spatial position, thereby providing a 3-dimensional cone-beam CT with fewer motion artifacts.

Certain implementations of the invention comprise computer processors which execute software instructions which cause the processors to perform a method of the invention. For example, one or more data processors may implement the methods of FIG. 4A and/or FIG. 8 by executing software instructions in a program memory accessible to the data processors. The invention may also be provided in the form of a program product. The program product may comprise any medium which carries a set of computer-readable signals comprising instructions which, when executed by a data processor, cause the data processor to execute a method of the invention. Program products according to the invention may be in any of a wide variety of forms. The program product may comprise, for example: physical media such as magnetic data storage media including floppy diskettes, hard disk drives, optical data storage media including CD ROMs, DVDs, electronic data storage media including ROMs, flash RAM, or the like. The computer-readable signals on the program product may optionally be compressed or encrypted.

Where a component (e.g. a software module, processor, assembly, device, circuit, etc.) is referred to above, unless otherwise indicated, reference to that component (including a reference to a “means”) should be interpreted as including as equivalents of that component any component which performs the function of the described component (i.e., that is functionally equivalent), including components which are not structurally equivalent to the disclosed structure which performs the function in the illustrated exemplary embodiments of the invention.

While a number of exemplary aspects and embodiments have been discussed above, those of skill in the art will recognize certain modifications, permutations, additions and sub-combinations thereof. For example:

-   -   In the embodiments described above, control points 32 used to         define a trajectory 30 are the same as the control points used         to perform the block 54 optimization process. This is not         necessary. For example, a simple trajectory 30, such as an arc         of gantry 16 about axis 18 (FIG. 1), may be defined by two         control points at its ends. While such control points may define         the trajectory, more control points will generally be required         to achieve an acceptable treatment plan. Accordingly, the block         54, 154 optimization processes may involve using different (e.g.         more) control points than those used to define the trajectory.     -   In the embodiments described above, constraints (e.g.         constraints on the changes in beam position/orientation         parameters between control points 32, constraints on the changes         in beam shape parameters between control points 32 and         constraints on the changes in the beam intensity between control         points 32) are used throughout the optimization processes 54,         154. In other embodiments, the optimization constraints may be         imposed later in the optimization process. In this manner, more         flexibility is available in meeting the optimization goals 61 in         an initial number of iterations. After the initial number of         iterations is performed, the constraints may be introduced. The         introduction of constraints may require that some beam         position/orientation parameters, beam shape parameters and/or         intensity parameters be changed, which may result in a need for         further optimization to meet the optimization goals 61.     -   In the embodiments described above, the beam position and beam         orientation at each control point 32 are determined prior to         commencing the optimization process 54, 154 (e.g. in blocks 52,         152) and are maintained constant throughout the optimization         process 54, 154 (i.e. optimization processes 54, 154 involve         varying and optimizing beam shape parameters and beam intensity         parameters, while trajectory 30 remains constant). In other         embodiments, the beam position and beam orientation parameters         (i.e. the set of motion axis positions at each control point 32)         are additionally or alternatively varied and optimized as a part         of optimization processes 54, 154, such that optimization         processes 54, 154 optimize the trajectory 30 of the radiation         delivery apparatus. In such embodiments, optimization processes         54, 154 may involve placing constraints on the available motion         axis positions and/or the rate of change of motion axis         positions between control points 32 and such constraints may be         related to the physical limitations of the particular radiation         delivery apparatus being used to deliver the dose to the subject         S.     -   In some embodiments, the radiation intensity may be held         constant and the optimization processes 54, 154 optimize the         beam shape parameters and/or the motion axis parameters. Such         embodiments are suitable for use in conjunction with radiation         delivery apparatus which do not have the ability to controllably         vary the radiation intensity. In some embodiments, the beam         shape parameters may be held constant and the optimization         processes 54, 154 optimize the intensity and/or the motion axis         parameters.     -   There are an infinite number of possible trajectories that can         be used to describe the position and orientation of a radiation         beam. Selection of such trajectories are limited only by the         constraints of particular radiation delivery apparatus. It is         possible to implement the invention using any trajectory capable         of being provided by any suitable radiation delivery apparatus.

It is therefore intended that the following appended claims and claims hereafter introduced are interpreted to include all such modifications, permutations, additions and sub-combinations as are within their true spirit and scope. 

1. A method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; specifying an initial plurality of control points along an initial trajectory which involves relative movement between a radiation source and the subject; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals to determine one or more radiation delivery parameters associated with each of the initial plurality of control points; and upon reaching one or more initial termination conditions: adding one or more additional control points to obtain an increased plurality of control points; iteratively optimizing the simulated dose distribution relative to the set of optimization goals to determine one or more radiation delivery parameters associated with each of the increased plurality of control points.
 2. A method according to claim 1 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the initial plurality of control points comprises iteratively optimizing the simulated dose distribution subject to one or more initial optimization constraints.
 3. A method according to claim 2 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the initial plurality of control points comprises one or more of: simulated annealing optimization; gradient-based optimization; optimization based on a genetic algorithm; and optimization based on a neural network.
 4. A method according to claim 2 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the increased plurality of control points comprises iteratively optimizing the simulated dose distribution subject to one or more subsequent optimization constraints.
 5. A method according to claim 4 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the increased plurality of control points comprises one or more of: simulated annealing optimization; gradient-based optimization; optimization based on a genetic algorithm; and optimization based on a neural network.
 6. A method according to claim 1 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the initial plurality of control points comprises, for each iteration: varying one or more of the radiation delivery parameters associated with one or more of the initial plurality of control points; determining the simulated dose distribution based on the one or more varied radiation delivery parameters; determining, on the basis of an optimization algorithm and the simulated dose distribution based on the one or more varied radiation delivery parameters, whether to accept or reject the one or more varied radiation delivery parameters; and if a determination is made to accept the one or more varied radiation delivery parameters, updating the current radiation delivery parameters to include the one or more varied radiation delivery parameters.
 7. A method according to claim 6 wherein varying one or more of the radiation delivery parameters associated with one or more of the initial plurality of control points is subject to one or more initial optimization constraints.
 8. A method according to claim 7 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the increased plurality of control points comprises, for each iteration: varying one or more of the radiation delivery parameters associated with one or more of the increased plurality of control points; determining the simulated dose distribution based on the one or more varied radiation delivery parameters; determining, on the basis of an optimization algorithm and the simulated dose distribution based on the one or more varied radiation delivery parameters, whether to accept or reject the one or more varied radiation delivery parameters; and if a determination is made to accept the one or more varied radiation delivery parameters, updating the current radiation delivery parameters to include the one or more varied radiation delivery parameters.
 9. A method according to claim 8 wherein varying one or more of the radiation delivery parameters associated with one or more of the increased plurality of control points is subject to one or more subsequent optimization constraints.
 10. A method according to claim 4 wherein the one or more radiation delivery parameters comprise one or more beam-shaping parameters.
 11. A method according to claim 10 wherein the one or more beam-shaping parameters comprise one or more configurations of a multi-leaf collimator.
 12. A method according to claim 11 wherein the one or more configurations of the multi-leaf collimator comprise positions of one or more leaves of the multi-leaf collimator.
 13. A method according to claim 12 wherein the initial and subsequent optimization constraints comprise position limitations on the one or more leaves of the multi-leaf collimator.
 14. A method according to claim 12 wherein the initial and subsequent optimization constraints comprise maximum changes in position of the one or more leaves of the multi-leaf collimator between successive control points.
 15. A method according to claim 12 wherein the initial and subsequent optimization constraints comprise maximum rates of change of position of the one or more leaves of the multi-leaf collimator per unit of relative motion between the radiation source and the subject.
 16. A method according to claim 4 wherein the one or more radiation delivery parameters comprise a beam intensity.
 17. A method according to claim 16 wherein the initial and subsequent optimization constraints comprise a maximum beam intensity.
 18. A method according to claim 16 wherein the initial and subsequent optimization constraints comprise maximum changes of beam intensity between successive control points.
 19. A method according to claim 16 wherein the initial and subsequent optimization constraints comprise maximum rates of change of beam intensity per unit of relative movement between the radiation source and the subject.
 20. A method according to claim 4 wherein the one or more radiation delivery parameters comprise a position of the radiation source relative to the subject.
 21. A method according to claim 20 wherein the initial and subsequent optimization constraints comprise one or more limitations on the position of the radiation source relative to the subject.
 22. A method according to claim 20 wherein the initial and subsequent optimization constraints comprise maximum changes in the position of the radiation source relative to the subject between successive control points.
 23. A method according to claim 20 wherein the initial and subsequent optimization constraints comprise maximum temporal rates of change in the position of the radiation source relative to the subject.
 24. A method according to claim 4 wherein at least one of the subsequent optimization constraints is different than a corresponding at least one of the initial optimization constraints.
 25. A method according to claim 24 wherein the at least one of the subsequent optimization constraints is more restrictive than the corresponding at least one of the initial optimization constraints.
 26. A method according to claim 1 comprising discontinuing the iterative optimization associated with increased plurality of control points upon reaching one or more subsequent termination conditions.
 27. A method according to claim 26 wherein: upon reaching the one or more initial termination conditions, a difference between the simulated dose distribution and the set of optimization goals is greater than an acceptable dose quality threshold; and before discontinuing the iterative optimization associated with the increased plurality of control points, the difference between the simulated dose distribution and the set of optimization goals is within the acceptable dose quality threshold.
 28. A method according to claim 26 comprising, after discontinuing the iterative optimization associated with the increased plurality of control points: providing the one or more radiation delivery parameters associated with the increased plurality of control points to a control system associated with a radiation delivery apparatus; effecting relative movement between the radiation source and the subject along a resultant trajectory; and delivering a radiation beam from the radiation source to the subject according to the radiation delivery parameters to impart a dose distribution on the subject.
 29. A method according to claim 28 wherein the resultant trajectory is the same as the initial trajectory.
 30. A method according to claim 28 wherein the resultant trajectory is different from the initial trajectory and is defined by the one or more radiation delivery parameters associated with each of the increased plurality of control points.
 31. A method according to claim 28 wherein effecting relative movement between the radiation source and the subject along the resultant trajectory comprises effecting non-planar relative movement between the radiation source and the subject.
 32. A method according to claim 28 wherein effecting relative movement between the radiation source and the subject along the resultant trajectory comprises effecting continuous relative movement between the radiation source and the subject along the resultant trajectory.
 33. A method according to claim 28 wherein effecting relative movement between the radiation source and the subject along the resultant trajectory comprises effecting non-self-overlapping relative movement between the radiation source and the subject.
 34. A method according to claim 28 wherein a start of the resultant trajectory and an end of the resultant trajectory comprise the same relative position between the radiation source and the subject and wherein effecting relative movement between the radiation source and the subject along the resultant trajectory comprises otherwise non-self-overlapping relative movement between the radiation source and the subject.
 35. A method according to claim 28 wherein effecting relative movement between the radiation source and the subject along the resultant trajectory comprises moving a plurality of motion axes of the radiation delivery apparatus.
 36. A method according to claim 28 wherein a number of the initial plurality of control points is insufficient to achieve an acceptable accuracy threshold between the simulated dose distribution and the imparted dose distribution and a number of the increased plurality of control points is sufficient to achieve the acceptable accuracy threshold between the simulated dose distribution and the imparted dose distribution.
 37. A method according to claim 1 wherein the one or more initial termination conditions comprise one or more of: a difference between the simulated dose distribution based on the radiation delivery parameters associated with the initial plurality of control points and the set of optimization goals is within an acceptable dose quality threshold; a threshold number of iterations; a threshold number of unsuccessful iterations wherein the simulated dose distribution based on the radiation delivery parameters associated with the initial plurality of control points does not approach the set of optimization goals; and a threshold number of successful iterations wherein the simulated dose distribution based on the radiation delivery parameters associated with the initial plurality of control points approaches the set of optimization goals.
 38. A method according to claim 26 wherein the one or more subsequent termination conditions comprise one or more of: a difference between the simulated dose distribution based on the radiation delivery parameters associated with the increased plurality of control points and the set of optimization goals is within an acceptable dose quality threshold; a threshold number of iterations; a threshold number of unsuccessful iterations wherein the simulated dose distribution based on the radiation delivery parameters associated with the increased plurality of control points does not approach the set of optimization goals; and a threshold number of successful iterations wherein the simulated dose distribution based on the radiation delivery parameters associated with the increased plurality of control points approaches the set of optimization goals.
 39. A method according to claim 26 comprising, after discontinuing the iterative optimization associated with the increased plurality of control points: adding one or more further additional control points to obtain a further increased plurality of control points; iteratively optimizing the simulated dose distribution relative to the set of optimization goals to determine one or more radiation delivery parameters associated with each of the further increased plurality of control points; and repeating adding one or more further additional control points and iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the further increased plurality of control points until ultimate termination conditions are reached.
 40. A method according to claim 39 wherein the ultimate termination conditions comprise one or more of: a difference between the simulated dose distribution based on the radiation delivery parameters associated with the further increased plurality of control points and the set of optimization goals is within an acceptable dose quality threshold; a threshold number of iterations; a threshold number of unsuccessful iterations wherein the simulated dose distribution based on the radiation delivery parameters associated with the further increased plurality of control points does not approach the set of optimization goals; a threshold number of successful iterations wherein the simulated dose distribution based on the radiation delivery parameters associated with the further increased plurality of control points approaches the set of optimization goals; and the further increased plurality of control points reaches a threshold number of control points.
 41. A method according to claim 1 wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the initial plurality of control points comprises simulating a dose contribution for at least one of the initial plurality of control points by: dividing a cross-sectional area of a beam-shape aperture into a plurality of two-dimensional beamlets; and simulating a dose distribution contribution from each of the plurality of two-dimensional beamlets; wherein at least two of the plurality of two-dimensional beamlets have different sizes.
 42. A method according to claim 41 wherein at least two of the plurality of two-dimensional beamlets have different shapes.
 43. A method according to claim 1 wherein the set of one or more optimization goals comprise at least one of: a desired total radiation output for a treatment of the subject; and a desired total time for a treatment of the subject.
 44. A method according to claim 28 comprising sensing a positional state of the subject and wherein delivering a radiation beam from the radiation source to the subject according to the radiation delivery parameters comprises: deactivating delivery of the radiation beam upon sensing that the position of the subject is outside of an acceptable range; and reactivating delivery of the radiation beam upon sensing that the position of the subject is within the acceptable range.
 45. A method according to claim 44 wherein effecting relative movement between the radiation source and the subject along the resultant trajectory comprises: deactivating relative movement between the radiation source and the subject upon sensing that the position of the subject is outside of the acceptable range; and reactivating relative movement between the radiation source and the subject upon sensing that the position of the subject is within the acceptable range.
 46. A method according to claim 28 comprising, while effecting relative movement between the radiation source and the subject, obtaining two-dimensional projection images of the target area at a plurality of locations along the resultant trajectory.
 47. A method according to claim 46 wherein obtaining two-dimensional projection images comprises, for each projection image, directing an imaging radiation beam toward the subject and sensing imaging radiation that is transmitted through the subject.
 48. A method according to claim 47 wherein the imaging radiation beam is generated by the radiation source.
 49. A method according to claim 47 wherein directing the imaging radiation beam toward the subject and delivering the radiation beam from the radiation source to the subject comprise time division multiplexing the imaging radiation beam and the radiation beam.
 50. A method according to claim 46 wherein the resultant trajectory comprises a 360° rotation of a gantry about the subject.
 51. A method for delivering radiation dose to a target area within a subject, the method comprising: defining a trajectory for relative movement between a radiation source and the subject; determining a radiation delivery plan; while effecting relative movement between the radiation source and the subject along the trajectory, delivering a radiation beam from the radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject, wherein delivering the radiation beam from the radiation source to the subject comprises varying at least one of an intensity of the radiation beam and a shape of the radiation beam over at least a portion of the trajectory; wherein effecting relative movement between the radiation source and the subject along the trajectory comprises one or more of: effecting non-planar relative movement between the radiation source and the subject; effecting continuous relative movement between the radiation source and the subject along the trajectory; effecting non-self-overlapping relative movement between the radiation source and the subject; wherein a start of the trajectory and an end of the trajectory comprise the same relative position between the radiation source and the subject and effecting otherwise non-self-overlapping relative movement between the radiation source and the subject; and moving a plurality of motion axes of a radiation delivery apparatus.
 52. A method according to claim 51 wherein determining the radiation delivery plan comprises: specifying a plurality of control points along the trajectory; defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points; and defining the radiation delivery plan, at least in part, on the basis of the one or more determined parameters associated with each of the control points.
 53. A method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; defining an initial trajectory for relative movement between a radiation source and the subject and an initial plurality of control points along the initial trajectory; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points; wherein the one or more radiation delivery parameters comprise a position of the radiation source relative to the subject and wherein iteratively optimizing the simulated dose distribution comprises defining an optimized trajectory for relative movement between the radiation source and the subject on the basis of the radiation delivery parameters.
 54. A method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; defining a trajectory for relative movement between a radiation source and the subject and a plurality of control points along the trajectory; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points; wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the control points comprises simulating a dose contribution for at least one particular control point by: dividing a cross-sectional area of a beam-shape aperture into a plurality of two-dimensional beamlets; and simulating a dose distribution contribution from each of the plurality of two-dimensional beamlets; wherein at least two of the plurality of two-dimensional beamlets have different sizes.
 55. A method according to claim 54 wherein at least two of the plurality of two-dimensional beamlets have different shapes.
 56. A method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; specifying a plurality of control points along a trajectory which involves relative movement between a radiation source and the subject; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals to determine one or more radiation delivery parameters associated with each of the plurality of control points; and upon reaching one or more constraint-addition conditions, adding one or more optimization constraints to the iterative optimization to determine one or more radiation delivery parameters associated with each of the plurality of control points subject to the one or more optimization constraints.
 57. A method for delivering radiation dose to a target area within a subject, the method comprising: defining a trajectory for relative movement between a treatment radiation source and the subject; determining a radiation delivery plan; while effecting relative movement between the treatment radiation source and the subject along the trajectory: delivering a treatment radiation beam from the treatment radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject, wherein delivering the treatment radiation beam from the treatment radiation source to the subject comprises varying at least one of an intensity of the treatment radiation beam and a shape of the treatment radiation beam over at least a portion of the trajectory; obtaining two-dimensional projection images of the target area at a plurality of locations along the trajectory.
 58. A method according to claim 57 wherein obtaining two-dimensional projection images comprises, for each projection image, directing an imaging radiation beam toward the subject and sensing imaging radiation that is transmitted through the subject.
 59. A method according to claim 58 wherein the imaging radiation beam is generated by the treatment radiation source.
 60. A method according to claim 58 wherein directing the imaging radiation beam toward the subject and delivering the treatment radiation beam from the treatment radiation source to the subject comprise time division multiplexing the imaging radiation beam and the treatment radiation beam.
 61. A method for delivering radiation dose to a target area within a subject, the method comprising: defining a trajectory for relative movement between a radiation source and the subject; determining a radiation delivery plan; sensing a positional state of the subject; while effecting relative movement between the radiation source and the subject along the trajectory, delivering a radiation beam from the radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject, wherein delivering the radiation beam from the radiation source to the subject comprises: varying at least one of an intensity of the radiation beam and a shape of the treatment radiation beam over at least a portion of the trajectory; deactivating delivery of the radiation beam upon sensing that the position of the subject is outside of an acceptable range; and reactivating delivery of the radiation beam upon sensing that the position of the subject is within the acceptable range.
 62. A method according to claim 61 wherein effecting relative movement between the radiation source and the subject along the trajectory comprises: deactivating relative movement between the radiation source and the subject upon sensing that the position of the subject is outside of the acceptable range; and reactivating relative movement between the radiation source and the subject upon sensing that the position of the subject is within the acceptable range.
 63. A method for delivering radiation dose to a target area within a subject, the method comprising: defining a trajectory for relative movement between a radiation source and the subject; determining a radiation delivery plan; sensing a positional state of the subject; while effecting relative movement between the radiation source and the subject along the trajectory, delivering a radiation beam from the radiation source to the subject according to the radiation delivery plan to impart a dose distribution on the subject, wherein delivering the radiation beam from the radiation source to the subject comprises: varying at least one of an intensity of the radiation beam and a shape of the treatment radiation beam over at least a portion of the trajectory; deactivating delivery of the radiation beam upon sensing that the position of the subject is outside of an acceptable range; and reactivating delivery of the radiation beam upon sensing that the position of the subject is within the acceptable range; and while effecting relative movement between the radiation source and the subject along the trajectory, obtaining two-dimensional projection images of the target area at a plurality of locations along the trajectory.
 64. A program product comprising computer readable instructions which, when executed by a processor, cause the processor to execute a method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; specifying an initial plurality of control points along an initial trajectory which involves relative movement between a radiation source and the subject; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals to determine one or more radiation delivery parameters associated with each of the initial plurality of control points; and upon reaching one or more initial termination conditions: adding one or more additional control points to obtain an increased plurality of control points; iteratively optimizing the simulated dose distribution relative to the set of optimization goals to determine one or more radiation delivery parameters associated with each of the increased plurality of control points.
 65. A program product comprising computer readable instructions which, when executed by a processor, cause the processor to execute a method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; defining an initial trajectory for relative movement between a radiation source and the subject and an initial plurality of control points along the initial trajectory; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points; wherein the one or more radiation delivery parameters comprise a position of the radiation source relative to the subject and wherein iteratively optimizing the simulated dose distribution comprises defining an optimized trajectory for relative movement between the radiation source and the subject on the basis of the radiation delivery parameters.
 66. A program product comprising computer readable instructions which, when executed by a processor, cause the processor to execute a method for planning delivery of radiation dose to a target area within a subject, the method comprising: defining a set of one or more optimization goals, the set of one or more optimization goals comprising a desired dose distribution in the subject; defining a trajectory for relative movement between a radiation source and the subject and a plurality of control points along the trajectory; iteratively optimizing a simulated dose distribution relative to the set of one or more optimization goals and subject to one or more initial optimization constraints to determine one or more radiation delivery parameters associated with each of the control points; wherein iteratively optimizing the simulated dose distribution to determine one or more radiation delivery parameters associated with each of the control points comprises simulating a dose contribution for at least one particular control point by: dividing a cross-sectional area of a beam-shape aperture into a plurality of two-dimensional beamlets; and simulating a dose distribution contribution from each of the plurality of two-dimensional beamlets; wherein at least two of the plurality of two-dimensional beamlets have different sizes.
 67. A method according to claim 12 wherein the one or more configurations of the multi-leaf collimator comprise one or more orientations of the multi-leaf collimator.
 68. A method according to claim 67 wherein the one or more orientations of the multi-leaf collimator comprise one or more orientations about an axis that is generally orthogonal to a plane of the one or more leaves of the multi-leaf collimator.
 69. A method according to claim 12 comprising maintaining an orientation of the multi-leaf collimator constant during iterative optimization.
 70. A method according to claim 69 wherein the constant orientation of the multi-leaf collimator is such that a movement axis of the one or more leaves of the collimator forms an angle spaced apart from 0° and spaced apart from 90° with respect to the initial trajectory at any given initial control point. 